Summary and Analysis

Geometry: 3-D Measurements

Problems

Problems

Volume for three-dimensional figures is the equivalent of
area for two-dimensional
figures. Volume is a three-dimensional measurement; that is, it measures the
combined length, width, and height of a figure. Because planes, polygons, and
other two-dimensional figures don't have height, they have no volume. Only
solids and figures with dimension greater than or equal to three have volume.

The unit for volume is the cubic unit. Liquid medicine is often measured in
cubic centimeters, whereas a swimming pool full of water may be measured in
cubic feet. One cubic unit is a cube with edges of length one. It looks
something like this:

Figure %: One cubic unit

Naturally, very few solids break down nicely into components of cubic units.
But just as polygons can be divided into triangles, polyhedra can be divided
into pyramids, and the volume of a pyramid is possible to calculate. In the
next lesson, we'll study the ways to
calculate the volume of polyhedra as well as spheres.